Technically featured image is custom field with name _thumbnail_id
that holds attachment ID. So you can easily query with something like:
$args = array(
'meta_query' => array(
array(
'key' => '_thumbnail_id',
)
)
);
$query = new WP_Query( $args );
Size on other hand is attribute of that attachment and not post itself. You will need to loop through attachment and get sizes they have (if I remember right it should be in data returned by wp_get_attachment_metadata()
).